The mass `m` of an electron is `9.1 xx 10^(31)kg` and the velocity `v` of an electron in the first Bohr orbit of a hydrogen atom is `2.2 xx 10^(6)ms^(-1)`. Assuming that the velocity is known within `10% (Deltav = 0.22 xx 10^(6)ms^(-1))`, calculate the uncertainty in the electron's position in a hydrogen atom.
Strategy: According to Heisenberg's principle, the uncertainty in the postion `(Deltax)` of any moving particle multiplied by the uncertainity of momentum `(Deltap_(x))` can never be less than `h//4pi`. In the given case, `Delta v` is known and we need to find `Deltax`.

Explanation

According to Eq.
`DeltaxDeltaV_(x) ge (h)/(4pim)`
`:. Deltax ge (h)/(4pim DeltaV_(x))`
`ge (6.63xx10^(-34)kg m^(2)s^(-1))/((4)(3.14)(9.1xx10^(-31)kg)(0.22xx10^(6)ms^(-1)))`
`ge 0.264 xx 10^(-9)m`
`ge 2.64xx10^(-10)m`
`ge 264 pm`